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Mathematics Concept & Skill Development Lecture Series: Webvideo consolidation of site lessons and lesson ideas in preparation. Price to be determined. Bright Students: Top universities want you. While many have high fees: many will lower them, many will provide funds, many have more scholarships than students. Postage is cheap. Apply and ask how much help is available. Caution: some programs are rewarding. Others lead nowhere. After acceptance, it may be easy or not to switch. Key Lessons forAbove links to lesson links in page borders. For Arithmetic
Deciml Place Value - funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6, US-CDN, UK-German and Metric SI style. For Algebra
What is
a Variable? - this entertaining oral & geometric view
may be before and besides more formal definitions - is the view mathematically
correct? |
www.whyslopes.com >> Volume 2 Three Skills For Algebra >> Chapter 13. Second Reading Guide Next: [Postscript-Unifying Theme - A Fourth Skill For Algebra.] Previous: [Chapter 12. Shorthand Usage Guide.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16][17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] Second Reading GuideVolume 2, Three Skills for Algebra The next chapters
give further examples and methods to strengthen and extend your algebraic way of writing and reasoning. Rules are introduced as they are needed. The fifth chapter Arithmetic Rules and Patterns for Algebra (algebraically described) describes how arithmetic properties, more precisely assumptions about arithmetic, can be employed in algebra along with the ideas of replacement and substitution. The properties are described symbolically. The previous chapters should give readers a mastery of the algebraic way of writing and thinking sufficient to understand the symbolic or algebraic statement of the properties or rules. The chapters can be read out of order if you wish. Some chapters, not always the first, may be easier than others. Remember what is not immediately understood by yourself might be well-known or easily understood by another. A Word of CautionThe following chapters show how algebraic way of writing and reasoning solves many problems of a similar type. Their solutions follow the same arithmetic or algebraic pattern. Yet a caution is required here. Once the derivation of a formula or the algebraic pattern of a solution was understood, I once thought computational examples to be a waste of time and energy — a distraction from the mastery of further algebraic patterns. To some extent this is true. But in physics, chemistry and business, a familiarity with the size and magnitudes of the numbers and quantities appearing in calculations is needed to avoid or spot simple numerical errors or hazards. This familiarity is only provided by doing some problems. Doing too many problems may leave insufficient time to learn and master the algebraic reasoning in a subject. www.whyslopes.com >> Volume 2 Three Skills For Algebra >> Chapter 13. Second Reading Guide Next: [Postscript-Unifying Theme - A Fourth Skill For Algebra.] Previous: [Chapter 12. Shorthand Usage Guide.] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16][17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] |
Road Safety Messages for All: When walking on a road, when is it safer to be on the side allowing one to see oncoming traffic? For students of reason in society, science and technology: Pattern Based Reason describes origins, benefits and limits of rule- and pattern-based thought and actions. Not all is certain. We may strive for objectivity, but not reach it. Postscripts offer a story-telling view of learning: [ A ] [ B ] [ C ] [ D ] to suggest how we share theories and practices. For Logic
These online chapters may amuse while leading to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics. For Geometry
Maps + Plans Use - Measurement use maps, plans and diagrams drawn
to scale. For Calculus
Why study slopes - this fall 1983 calculus appetizer shone in many
classes at the start of calculus. It could also be given after the intro of slopes
to introduce function maxima and minima at the ends of closed intervals. |